The charity special was filmed for Comic Relief and won't be aired until March - three months after Ross's suspension is over.
Sir Alan Sugar offered Ross the role in May. The presenter has not received any payment for taking part.
A BBC insider told The Mirror: "Jonathan was in a difficult position as his suspension came just days before filming began on the show. Pulling out at such short notice would have left producers with a headache."
A spokesman added: "The BBC agreed to Jonathan Ross taking part in an advance recording of Comic Relief Does The Apprentice. The BBC did not wish to disadvantage the charity."